CN115275754A - Free electron laser and micro undulator - Google Patents

Free electron laser and micro undulator Download PDF

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CN115275754A
CN115275754A CN202210758448.4A CN202210758448A CN115275754A CN 115275754 A CN115275754 A CN 115275754A CN 202210758448 A CN202210758448 A CN 202210758448A CN 115275754 A CN115275754 A CN 115275754A
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grating
undulator
micro
electron beam
laser
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林宏翔
魏晓慧
廖天发
王文辕
杜娟
杨明亮
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Huizhou University
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
    • H01S3/09—Processes or apparatus for excitation, e.g. pumping
    • H01S3/0903—Free-electron laser
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24—Coupling light guides
    • G02B6/42—Coupling light guides with opto-electronic elements
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/24—Coupling light guides
    • G02B6/42—Coupling light guides with opto-electronic elements
    • G02B6/4201—Packages, e.g. shape, construction, internal or external details
    • G02B6/4216—Packages, e.g. shape, construction, internal or external details incorporating polarisation-maintaining fibres
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S3/00—Lasers, i.e. devices using stimulated emission of electromagnetic radiation in the infrared, visible or ultraviolet wave range
    • H01S3/005—Optical devices external to the laser cavity, specially adapted for lasers, e.g. for homogenisation of the beam or for manipulating laser pulses, e.g. pulse shaping

Abstract

The invention relates to a micro undulator of a free electron laser, wherein the free electron laser comprises an optical processing unit which can output X-direction polarized laser light and the micro undulator which is used for generating a periodically-changed transverse deflection electric field to deflect an electron beam injected along a Z direction. The micro undulator comprises a reflecting layer, a substrate layer positioned above the reflecting layer and a grating positioned on the substrate layer, wherein the grating is arranged in the incidence direction of the electron beams. The free electron laser adopts the micro undulator, and the size of the micro undulator can be made small due to the adoption of optical constraint instead of the traditional magnetic constraint, so that the size of the free electron laser is reduced. The period of the micro undulator is smaller than that of the undulator formed by a conventional magnetic element, and the requirements on electron beam energy can be reduced when coherent radiation light is generated.

Description

Free electron laser and micro undulator
Technical Field
The invention relates to a free electron laser and a micro undulator thereof.
Background
The free electron laser light source is a novel coherent light source, has the advantages of wide working wavelength range, pure frequency spectrum, high power and the like, and has great application requirements in the fields of biology, materials, medicine and the like, so that the free electron laser technology is rapidly developed since the invention of the free electron laser theory in the 70 s of the 20 th century. John Madey (John Madey) in 1971 proposed a Free Electron Laser (FEL) device that produced relevant radiation using relativistic electron beams in a undulator, followed by experiments at stanford university that confirmed the amplifier and resonator principle of FEL, achieving a gain of 7% at a wavelength of 10 um. Then, a plurality of research institutions in the world also develop the research on the FEL oscillators in the infrared and terahertz wave bands, and with the development of photocathode microwave electron guns and beam compression technologies, the beam quality of a linear accelerator is continuously improved, so that a foundation is laid for free electron lasers with short wavelength (nm) and ultra-short wavelength (less than 0.1 nm). In 1983, the Self-Amplified Spontaneous emission (SASE) scheme of X-ray coherent Radiation is realized by using a high-gain mode through the interaction between Spontaneous emission at the tail of an electron beam as a seed laser and a head electron beam, which is proposed by Bonefagao (Bonifacio), narducci (Narducci) and Pellegini (Pellegrini). In 1992 Pelegrini (Pellegrini) proposed the use of a Stanford linac to generate high quality electron beams to achieve SASE. In 2009, the first X-ray free electron laser-Linear Coherent Light Source (LCLS) was born in the united states. After 2010, a free electron laser light source is raised worldwide to build a hot tide, and a plurality of high-performance free electron laser devices are sequentially used for debugging light, such as Korean PAL-XFEL, swiss-FRL, european-XFEL and the like. In the free electron laser, a high-energy electron beam passes through a periodically arranged magnetic field (undulator) to generate laser gain, so the undulator is an essential component in the free electron laser, and the free electron lasers built at present all adopt the undulator formed by a periodic magnet.
However, the size of the conventional undulator is very large, and thus it is necessary to provide an undulator having a small size.
Disclosure of Invention
The invention aims to provide a free electron laser with a miniature undulator and the miniature undulator thereof.
An XYZ space rectangular coordinate system is defined, and a free electron laser includes an optical processing unit and a micro undulator. The optical processing unit is used for carrying out preset optical processing on incident laser to output X-direction polarized light. The miniature undulator is used for generating a periodically-changed transverse deflection electric field to deflect an electron beam injected along the Z direction. Wherein the micro undulator includes a reflective layer parallel to a plane defined by the X-axis and the Z-axis, a base layer on the reflective layer, and a grating on the base layer. The grating is distributed along the injection direction of the electron beam, and the grating grooves are parallel to the X axis.
As an implementation manner, the tooth thickness of two grating protrusions located at two ends of the grating is d, the tooth thickness of the grating protrusion located between the two grating protrusions located at two ends of the grating is 2d, the width of each grating groove is 2d, the number of grating protrusions with the tooth thickness of 2d is an odd number, and d is a number greater than zero.
In one embodiment, the laser has a wavelength equal to the period of the grating, and the grating has a tooth thickness that is half the period of the grating.
In one embodiment, the center of the electron beam is close to the grating surface.
As an embodiment, the distance between the center of the electron beam and the grating surface is λ/4, where λ is the wavelength of the laser light, the grating satisfies the following relationship:
Figure BDA0003720325000000021
wherein N is the refractive index of the grating, H is the grating tooth height, W is the thickness of the substrate layer, and N and m are positive integers.
A micro undulator includes a reflective layer parallel to a plane defined by an X-axis and a Z-axis, a substrate layer on the reflective layer, and a grating on the substrate layer.
As an implementation manner, the tooth thickness of two grating protrusions located at two ends of the grating is d, the tooth thickness of the grating protrusion located between the two grating protrusions located at two ends of the grating is 2d, the width of each grating groove is 2d, and the number of grating protrusions with the tooth thickness of 2d is an odd number.
In one embodiment, the grating is a silicon grating.
As an embodiment, defining an electron beam passing above the grating, and laser irradiating the grating from a direction parallel to lines of the grating, wherein an arrangement direction of the grating is parallel to an incident direction of the electron beam, a distance between a center of the electron beam and a grating surface is λ/4, where λ is a wavelength of the laser, the grating satisfies the following relationship:
Figure BDA0003720325000000022
wherein N is the refractive index of the grating, H is the grating tooth height, W is the thickness of the substrate layer, and N and m are positive integers.
In one embodiment, the material of the reflective layer is silver, and the material of the base layer is the same as the material of the grating.
Compared with the prior art, the free electron laser adopts the micro undulator, and the size can be made small because the micro undulator adopts optical constraint instead of traditional magnetic constraint, thereby further reducing the size of the free electron laser. The period of the micro undulator is smaller than that of the undulator formed by a conventional magnetic element, and the requirements on the energy of electron beams can be reduced when coherent radiant light is generated.
Drawings
FIG. 1 is a schematic diagram of the structure and electron beam trajectory of a free electron laser according to the present invention.
Fig. 2 is a schematic diagram of the structure, parameters and laser path of the grating of the micro undulator of the free electron laser according to the present invention.
FIG. 3 is a diagram showing the distribution of the transverse deflection electric field Ex at the center of the electron beam trajectory (y =1.875 um) in the electromagnetic field simulation of an embodiment.
FIG. 4 is a diagram illustrating distribution of the transverse deflection electric field Ex in the electromagnetic field simulation according to an embodiment.
FIG. 5 is a distribution diagram of an electron beam in an initial state during electron beam tracking calculations performed by the GPT software in one embodiment.
FIG. 6 is a graph illustrating the clustering of electron beams after a number of raster periods as they undergo electron beam tracking calculations by the GPT software in one embodiment.
Detailed Description
A free electron laser and a micro-undulator according to the present invention will be described in further detail with reference to the following embodiments and accompanying drawings.
The free electron laser mainly includes a radiation source for generating laser light, an optical processing unit for performing a predetermined optical process on the laser light generated by the radiation source, an electron beam generator for generating an electron beam, a linear accelerator, a microwave device, a vacuum system, and a micro-undulator. Referring to fig. 1, for the convenience of observation, the present embodiment omits a radiation source, an electron beam generator, a linear accelerator, a microwave device, and a vacuum system, simplifies the structure of the optical processing unit, is only illustrated by a lens, and defines an XYZ spatial rectangular coordinate system to help explain the specific structures of the free electron laser and the micro-oscillator. It will be appreciated that the radiation source, electron beam generator, linear accelerator, microwave device, vacuum system and optical treatment unit may be conventional.
The optical processing unit is used for screening the X-direction line bias laser in the short-pulse femtosecond laser pulse and irradiating the micro-undulator from the + Y-direction side of the micro-undulator.
The electron beam output from the electron beam generator is emitted from the-Z direction side toward the + Z direction side of the micro undulator.
When the micro oscillator is irradiated by femtosecond laser pulse, a transverse deflection electric field with sine periodic variation along the Z direction can be generated, so that an electron beam injected along the Z direction is deflected under the modulation action of the transverse deflection electric field with the periodic variation, periodic oscillation is generated, coherent electromagnetic waves are radiated outwards, and laser gain is realized. In this embodiment, the micro undulator mainly includes a reflective layer, a substrate layer, and a grating.
The reflecting layer is parallel to the plane defined by the X axis and the Z axis and can be made of reflecting materials such as metal silver and the like.
The substrate layer is located on the reflecting layer, namely the + Y direction side of the reflecting layer, and the material of the substrate layer is the same as that of the grating, and the substrate layer is used for being matched with the grating to form a preset optical path difference.
The grating is formed on the base layer, i.e., the + Y direction side of the base layer.
In order to obtain a better laser gain, the period of the grating should be equal to the wavelength λ of the laser, i.e., a + B = λ, where a and B are the sizes of two portions (grating protrusions and grating grooves) in one period of the grating, respectively, a is the width (tooth thickness) of the grating protrusion portion in the Z-axis direction, and B is the width (spacing between grating protrusions) of the grating groove in the Z-axis direction. Furthermore, the tooth thickness of the grating may be half the period of the grating. Thus, when the electron beam passes half the grating period length, the surface electric field created by the laser is just reversed. At this time, if the phase slip caused by the lateral velocity is not considered (when the number of undulator periods is small), the electric field force does zero to the electron beam within one grating period length, and after two grating period lengths, the electron beam returns to the center of the track (see the electron beam track in fig. 1).
In this embodiment, the thickness of the teeth of the grating protrusions closest to the electron beam generator and farthest from the electron beam generator is set to be d, the thickness of the teeth of the grating protrusions between the two is set to be 2d, and the width of the grating groove is set to be 2d. And the number of grating protrusions with the tooth thickness of 2d is odd. Thus, the length of the entire grating is a positive integer multiple of the grating period, grating period a + B =4d = λ. So configured, it is ensured that the electron beam is a sinusoidal trajectory in the Z-direction during the movement. d is a number greater than zero.
The gratings are distributed along the direction of incidence of the electron beam, the center of the electron beam is close to the surface of the gratings, and the mutually parallel slits (grooves or grating lines) between the gratings are also parallel to the X axis, so that the electron beam can be subjected to a larger transverse deflection electric field. In this embodiment, the distance between the center of the electron beam and the surface of the grating is h = λ/4, and the grating satisfies the following condition:
Figure BDA0003720325000000041
wherein N is the refractive index of the grating, H is the height of the grating teeth, W is the thickness of the substrate layer, and N and m are positive integers. When the condition of the first expression in the formula is satisfied, a coherently intensified electric field can be generated at the electron beam trajectory position (y =1.875 um). The opposite phase can be generated in the adjacent half of the grating period when the condition of the second expression in the formula is satisfied.
According to the formula, the dielectric constant can be determined according to the refractive index n of the grating, and the materials of the grating and the substrate layer of the micro-undulator can be further determined, wherein the material adopted in the embodiment is silicon dioxide (SiO)2)。
Thus, when the grating surface is irradiated with the X-direction polarized light from the Y-axis direction, a sinusoidal-period transverse electric field distribution can be formed on the grating surface along the Z-axis direction
Figure BDA0003720325000000042
At the same time, has a correlation with time, where EinIs the maximum amplitude of the electric field, omega is the angular frequency of the electric field, omega0For the initial angular frequency of the electric field, t and z are times,. Phi0And phi0Is the initial phase of the electric field. Because the polarization characteristic of the incident laser and the grating groove direction are along the X-axis direction, the electric field in the Z-axis direction and the electric field in the Y-axis direction are both zero, namely Ez＝Ey=0. According to the equation of motion of the electron beam
Figure BDA0003720325000000043
(where γ is Lorentz factor (relativistic energy factor), meIs a static mass of electrons and is,
Figure BDA0003720325000000044
as the velocity of the electrons, is,
Figure BDA0003720325000000045
for the electric field, q is the amount of charge), substituting the electric field expression into the equation, one can obtain the second differential of x with respect to time t:
Figure BDA0003720325000000046
and further solving an electron beam trajectory equation in the X-axis direction:
Figure BDA0003720325000000051
order to
Figure BDA0003720325000000052
c is the speed of light, β represents the ratio of the particle speed of the electron beam to the speed of light, β x represents the ratio of the particle speed in the x direction to the speed of light, β y represents the ratio of the particle speed in the y direction to the speed of light, and there are:
Figure BDA0003720325000000053
according to the speed synthesis relation, performing Taylor expansion on the speed synthesis relation, and keeping a first-order approximation to obtain
Figure BDA0003720325000000054
In order to cause radiation-dependent intensification of the electron beam, the grating period λu= A + B and coherent radiation wavelength λsShould satisfy
Figure BDA0003720325000000055
Wherein theta is the radiation angle of the free electron laser, generally theta is a minimum value, cos theta is equal to 1 approximately, namely, the distance lambda is separateduHaving a wavelength of the two electron beam radiationInteger multiple relation, from which
Figure BDA0003720325000000056
(paraxial approximation, the radiation angle is zero), and the coherent radiation wavelength analytic expression can be obtained by combining the expressions (1) and (2):
Figure BDA0003720325000000057
compared with the radiation resonance formula of free electron laser, the micro undulator of the invention can be found to have a similar analytic form, but more higher harmonic terms. In conventional undulators, a high-energy electron beam (γ > 1) can be used to generate the radiation wavelength λsMuch less than the undulator period λuThe free electron laser of the invention, while for the micro undulator, because the undulator period is much shorter than that of the conventional undulator, it can be known from the form of the radiation wavelength that the free electron laser with the same wavelength is generated, the electron beam energy required by the micro undulator of the invention is lower.
In one embodiment, the laser and grating parameters in table one are selected, and the electric field distribution of the grating surface is obtained by using an electromagnetic field simulation software, such as ANSYS mechanical FDTD or COMSOL or CST simulation, and fig. 3-4 show the simulation results, it can be seen that at the center of the electron beam trajectory (y =1.875 um), the Ex component is large and exhibits periodic variation, and the Ez component is close to zero, which meets the expected design requirement.
Table-laser and raster parameters
Figure BDA0003720325000000061
Based on the grating surface electric field obtained by the previous simulation, the electron beam Tracking calculation is performed by utilizing GPT (General Particle Tracking, GPT) software (the parameters are shown in the table II), the flow intensity of the electron beam is set to be 10mA, the energy of the electron beam is set to be 10MeV, the electron beam is uniformly distributed at the beginning, and the electron beam is observed to generate obvious clustering after 6 grating cycles, and the relativity factor of the electron beam is reduced by 0.15 (shown in reference to fig. 5-6).
According to the Madey theorem in free electron laser theory:
Figure BDA0003720325000000062
wherein gamma isf、γiThe energy of the electrons before and after the interaction respectively, subscripts 1 and 2 respectively represent the first-order perturbation term and the second-order perturbation term of the power expansion of the light field,<>representing the averaging of the initial phases of all electrons with respect to the light field. Since the theorem is based on the energy change of electron interaction, the magnetic vector operation of the undulator is not designed, and thus the micro-undulator can be used in the present invention. The left side of the equation is the electron beam average energy loss, and the right side of the equation is the energy variation dispersion, which is further based on the formula of spontaneous emission intensity:
Figure BDA0003720325000000063
in combination with energy conservation, the light field small signal gain can be obtained:
Figure BDA0003720325000000064
the simulated relativistic factors and other parameters are substituted to obtain the normalized energy gain of about 0.3. Where P is power, Ω is solid angle, es is radiation field intensity, and δ is used to represent the variation of γ.
TABLE-II electron beam tracking calculation parameters
Figure BDA0003720325000000065
In the above embodiment, the thickness of the teeth of the two grating protrusions at the two ends of the grating is d, the thickness of the teeth of all the grating protrusions in the middle is 2d, and the width of the grating groove is 2d. And the number of grating protrusions with the tooth thickness of 2d is odd. It is understood that in other embodiments, all grating protrusions may have the same tooth thickness, for example, all grating protrusions have a width of 2d, all grating grooves have a width of 2d, and the number of grating protrusions is even. In this case, the electric field deflection causes the electron beam to have a transverse velocity, and the electron beam is deflected from the Z axis to the + X axis or the-X axis during the movement thereof in a sinusoidal trajectory. It is only necessary to adjust the position of the product component according to the electron beam trajectory.
In summary, the free electron laser of the invention adopts the micro undulator, the micro undulator deflects the electron beam by the electric field of the femtosecond laser on the grating surface, instead of the traditional magnetic confinement, and the size of the micro undulator is extremely small because the wavelength phase of the laser is in the um magnitude, thereby reducing the size of the free electron laser. The period of the micro undulator is smaller than that of the undulator formed by a conventional magnetic element, and the requirements on the energy of electron beams can be reduced when coherent radiant light is generated. In addition, the invention also provides an analytical expression of the coherent radiation wavelength of the electron beam, which can accurately solve the relation among the energy, the structure and the wavelength of the electron beam and determine the parameters such as the laser frequency, the energy of the electron beam and the like required by the miniature undulator. The medium material and corresponding size required by the micro undulator can be determined by those skilled in the art according to the central position of the electron beam track and the laser wavelength and the formula of the equation system.
While the invention has been described in conjunction with the specific embodiments set forth above, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art in light of the foregoing description. Accordingly, it is intended to embrace all such alternatives, modifications, and variations that fall within the spirit and scope of the appended claims.

Claims (10)

1. A free electron laser defining an XYZ spatial cartesian coordinate system, comprising:
an optical processing unit for performing a preset optical process on the incident laser light to output X-direction polarized light; and
a micro undulator for generating a periodically varying lateral deflection electric field to deflect the electron beam incident in the Z direction; wherein the micro undulator includes:
a reflective layer parallel to a plane defined by the X-axis and the Z-axis;
a base layer over the reflective layer; and
and the gratings are distributed along the incidence direction of the electron beams, and the grating grooves are parallel to the X axis.
2. The free electron laser of claim 1, wherein the two grating protrusions at both ends of the grating have a tooth thickness of d, the two grating protrusions between the two grating protrusions at both ends of the grating have a tooth thickness of 2d, the grating grooves have a width of 2d, and the number of grating protrusions having a tooth thickness of 2d is an odd number, wherein d is a number greater than zero.
3. The free electron laser of claim 1, wherein the laser light has a wavelength equal to the period of the grating and the grating has a tooth thickness of one half of the period of the grating.
4. The free electron laser of claim 1, wherein a center of the electron beam is proximate to the grating surface.
5. The free electron laser of claim 1, wherein the center of the electron beam is at a distance λ/4 from the grating surface, where λ is the wavelength of the laser light, and the grating satisfies the following relationship:
Figure FDA0003720324990000011
wherein N is the refractive index of the grating, H is the grating tooth height, W is the thickness of the substrate layer, and N and m are positive integers.
6. A micro undulator, comprising:
a reflective layer parallel to a plane defined by the X-axis and the Z-axis;
a base layer over the reflective layer; and
a grating located on the base layer.
7. The micro-undulator of claim 6, wherein the two grating protrusions located at both ends of the grating have a tooth thickness of d, the two grating protrusions located between the two grating protrusions located at both ends of the grating have a tooth thickness of 2d, the grating grooves have a width of 2d, and the number of grating protrusions having a tooth thickness of 2d is an odd number.
8. The micro-undulator of claim 6, wherein the grating is a silicon grating.
9. The micro-undulator of claim 6, wherein an electron beam is defined to pass over the grating and laser light irradiates the grating from a direction parallel to the lines of the grating, wherein the grating is arranged parallel to the incident direction of the electron beam, the center of the electron beam is spaced from the grating surface by a distance λ/4, where λ is the wavelength of the laser light, and the grating satisfies the following relationship:
Figure FDA0003720324990000021
wherein N is the refractive index of the grating, H is the grating tooth height, W is the thickness of the substrate layer, and N and m are positive integers.
10. The micro-undulator of claim 6, wherein the material of the reflective layer is silver and the material of the base layer is the same as the material of the grating.
CN202210758448.4A 2022-06-29 2022-06-29 Free electron laser and micro undulator Pending CN115275754A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20230029210A1 (en) * 2021-07-22 2023-01-26 National Tsing Hua University Dielectric-grating-waveguide free-electron laser

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20230029210A1 (en) * 2021-07-22 2023-01-26 National Tsing Hua University Dielectric-grating-waveguide free-electron laser

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